Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:

n = int(input())

fn = []
k=1
while True:
    num = (k*(k+1))//2
    if num>n:
        break
    fn.append(num)
    k+=1
i=0
j=len(fn)-1

while i<=j:
    if fn[i]+fn[j]==n:
        print("YES")
        break
    elif fn[i]+fn[j]<n:
        i+=1
    else:
        j-=1

if i>j or fn[i]+fn[j]!=n:
    print("NO")